解方程组

通过使用scipy.optimize中的fsolve函数或broyden1函数，解三元方程组的解，并将解代入原方程验证（f1,f2,f3均接近于0），程序代码：

import scipy.optimize as opt
from numpy import exp
import timeit
st1 = timeit.default_timer()
def f(variables):  
    (x, y,z) = variables
    first_eq = x + y**2 +2*z- 4    
    second_eq = exp(x) + x*y-z**2 - 3    
    third_eq=x**2-y*z+z**2-2    
    return [first_eq, second_eq,third_eq]

solution = opt.fsolve(f, (0.1,0.5,1))  # solution = opt.broyden1(f,(0.1,0.5,1))
print(solution)
st2 = timeit.default_timer()
print("RUN TIME : {0}".format(st2-st1))
x, y, z = solution[0],solution[1],solution[2]
print(f'f1={f((x,y,z))[0]}')
print(f'f2={f((x, y, z))[1]}')
print(f'f3={f((x, y, z))[2]}')

运行结果：

[1.2298751 0.70637 1.13558316]

RUN TIME : 0.0009333000000000258

f1=-2.9887203822909214e-13

f2=-3.907985046680551e-14

f3=2.05613304160579e-13